Well-posedness of one-way wave equations and absorbing boundary conditions. (English) Zbl 0618.65077

Trefethen, Lloyd N.; Halpern, Laurence

Math. Comput. 47, 421-435 (1986).

A method for constructing one-way wave equations is suggested. A one-way wave equation is a partial differential equation which in some sense behaves like the wave equation in one direction but permits no propagation in the opposite one. The authors investigate conditions under which the initial value problem for the one-way wave equations and the initial-boundary value problem for the two-dimensional wave equation in the domain \(x\geq 0\), \(t\geq 0\) with one-way equations as boundary condition are well posed.

Reviewer: Yu.Shokin

MSC:

65N06	Finite difference methods for boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L05	Wave equation
76Q05	Hydro- and aero-acoustics

Keywords:

well-posedness; absorbing boundary condition; paraxial approximation; parabolic approximation; rational approximation; Padé table; migration; underwater acoustics; one-way wave equations